Question

How many 5 digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digits appears more than once ?

Answer 1

From the 5 digit telephone number, the firtst two digit have to be 6,7 as give in the question

Therefore we have only choices in choosing last 3 digits out of numbers from 0 to 9 except 6 and 7

There are 10 digits from 0 to 9

Hence Total nos. to be taken to fill the last three digits= 10-2 = 8

Hence total permutations of arranging last 3 numbers from 8 is 8P3 = 8!/(8-3)! = 8 x 7 x 6 = 336


or

It is given that the 5-digit telephone numbers always start with 67.

Therefore, there will be as many phone numbers as there are ways of filling 3 vacant places

There are 10 digits from 0 to 9

I place after 67 can be filled in 8 ways.

II place after 67 can be filled in 7 ways.

III place after 67 can be filled in 6 ways.

∴ No of telephone numbers that can be constructed.

⇒8×7×6⇒8×7×6

⇒336 Ans.